1. **Problem Statement:** Determine if each given set is finite or infinite. If finite, find its cardinality. 2. **Set (a):** $\{1, 2, 3, \ldots, 30\}$ - This set lists all integers from 1 to 30. - Since it has a first element and a last element, and all elements are listed explicitly, it is a finite set. - The cardinality is the number of elements, which is 30. 3. **Set (b):** $\{22, 23, 24, 25, \ldots\}$ - This set starts at 22 and continues indefinitely. - There is no last element, so the set is infinite. 4. **Set (c):** The set of even numbers greater than 29. - Even numbers greater than 29 are $30, 32, 34, \ldots$ but since 30 is not greater than 29, the first element is 30 or 32? - Actually, 30 is even but not greater than 29, so the first even number greater than 29 is 30 (since 30 > 29). - The set continues indefinitely with even numbers increasing without bound. - Therefore, the set is infinite. **Final answers:** - (a) Finite, cardinality 30 - (b) Infinite - (c) Infinite